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Number of distinct automorphism group sizes for binary self-dual codes of length 2n.
5

%I #15 Jan 07 2019 05:55:27

%S 1,1,1,2,2,3,4,7,9,16,24,48,85,149,245,388

%N Number of distinct automorphism group sizes for binary self-dual codes of length 2n.

%C Codes are vector spaces with a metric defined on them. Specifically, the metric is the hamming distance between two vectors. Vectors of a code are called codewords.

%C A code is usually represented by a generating matrix. The row space of the generating matrix is the code itself.

%C Self-dual codes are codes such all codewords are pairwise orthogonal to each other.

%C Two codes are called permutation equivalent if one code can be obtained by permuting the coordinates (columns) of the other code.

%C The automorphism group of a code is the set of permutations of the coordinates (columns) that result in the same identical code.

%H W. Cary Huffman and Vera Pless, <a href="https://doi.org/10.1017/CBO9780511807077">Fundamentals of Error Correcting Codes</a>, 2003, pp. 7, 252-330, 338-393.

%e There are a(16) = 388 distinct sizes for the automorphism groups of the binary self-dual codes of length 16. In general, two automorphism groups with the same size are not necessarily isomorphic.

%Y Cf. self-dual codes A028362, A003179, A106162, A028363, A106163.

%K nonn,more

%O 1,4

%A _Nathan J. Russell_, Dec 02 2018